Fast parametric two-qubit gates for fixed-frequency qubits and tunable couplers, part 1: theory

The parametric gates implemented using flux-tunable transmon couplers offer flexibility and access to large native gate sets for fixed-frequency qubits. However, no clear guiding principle has been found for locating optimal points in parameter space for these gates, typically forcing a tradeoff between gate times and high fidelities. With current devices displaying relatively short coherence times, it is necessary to escape that tradeoff. In this talk, we present a method for doing so by controlling the different harmonics of the coupler's frequency response to the flux. The solutions consist of simple analytical expressions relating the parameters of the drive among each other, as well as to the design parameters of the device.